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Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes

Part of: Markov processes Mathematical economics Stochastic analysis

Published online by Cambridge University Press:  11 December 2019

Pierre-Olivier Goffard  and
Andrey Sarantsev
Pierre-Olivier Goffard*
Affiliation:
Université Lyon 1
Andrey Sarantsev*
Affiliation:
University of Nevada, Reno
*
*Postal address: LSAF EA2429, Université Lyon 1, 50 Avenue Tony Garnier, Institut de Science Financière et d’Assurances, F-69007 Lyon, France. Email address: pierre.olivier.goffard@gmail.com
**Postal address: Department of Mathematics and Statistics, University of Nevada, Reno, 1664 North Virginia Street, NV 89557, USA. Email address: asarantsev@unr.edu
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Abstract

We find explicit estimates for the exponential rate of long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality allows us to reduce the problem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyapunov functions.

Keywords

Ruin probabilityuniform ergodicityLyapunov functionstochastically ordered processSiegmund duality

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60H10: Stochastic ordinary differential equations 60J60: Diffusion processes 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 4 , December 2019 , pp. 1244 - 1268
Copyright
© Applied Probability Trust 2019 

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